We apply a wide-field quantitative phase microscopy technique based on parallel two-step phase-shifting on-axis interferometry to visualize live biological cells and microorganism dynamics. The parallel on-axis holographic approach is more efficient with camera spatial bandwidth consumption compared to previous off-axis approaches and thus can capture finer sample spatial details, given a limited spatial bandwidth of a specific digital camera. Additionally, due to the parallel acquisition mechanism, the approach is suitable for visualizing rapid dynamic processes, permitting an interferometric acquisition rate equal to the camera frame rate. The method is demonstrated experimentally through phase microscopy of neurons and unicellular microorganisms.